mlsanityData to 7 Oct 2026

Properties of Discrete Sliced Wasserstein Losses

arXiv 2307.10352 ↗First posted 19 Jul 2023stat.ML cs.LG math.OCcited by 12

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Abstract (arXiv)

The Sliced Wasserstein (SW) distance has become a popular alternative to the Wasserstein distance for comparing probability measures. Widespread applications include image processing, domain adaptation and generative modelling, where it is common to optimise some parameters in order to minimise SW, which serves as a loss function between discrete probability measures (since measures admitting densities are numerically unattainable). All these optimisation problems bear the same sub-problem, which is minimising the Sliced Wasserstein energy. In this paper we study the properties of E: Y longmapsto SW22(γY, γZ), i.e. the SW distance between two uniform discrete measures with the same amount of points as a function of the support Y ∈ ℝn × d of one of the measures. We investigate the regularity and optimisation properties of this energy, as well as its Monte-Carlo approximation Ep (estimating the expectation in SW using only p samples) and show convergence results on the critical points of Ep to those of E, as well as an almost-sure uniform convergence and a uniform Central Limit result on the process Ep(Y). Finally, we show that in a certain sense, Stochastic Gradient Descent methods minimising E and Ep converge towards (Clarke) critical points of these energies.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 18 of its 40 references that are in the map. First posted on arXiv 19 Jul 2023.

Builds on

18 of 40 references.

References · 18

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  3. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  4. 2017Improved Training of Wasserstein GANscited by 2,223
  5. 2018Computational Optimal Transportcited by 765
  6. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
  7. 2018Generative Modeling using the Sliced Wasserstein Distancecited by 108
  8. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 83
  9. 2018Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusionscited by 77
  10. 2019Conservative set valued fields, automatic differentiation, stochastic gradient method and deep learningcited by 71
  11. 2021Minibatch optimal transport distances; analysis and applicationscited by 62
  12. 2019Sliced Wasserstein Generative Modelscited by 61
6 more
  1. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  2. 2020Convergence of constant step stochastic gradient descent for non-smooth non-convex functionscited by 27
  3. 2019Approximate Bayesian Computation with the Sliced-Wasserstein Distancecited by 22
  4. 2018Analysis of nonsmooth stochastic approximation: the differential inclusion approachcited by 21
  5. 2021Non-asymptotic convergence bounds for Wasserstein approximation using point cloudscited by 9
  6. 2016Estimating orthant probabilities of high dimensional Gaussian vectors with an application to set estimationcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 4; 2026: 3.

12 papers.

  1. 2025A Novel Sliced Fused Gromov-Wasserstein Distancecited by 9
  2. 2023Convergence of SGD for Training Neural Networks with Sliced Wasserstein Lossescited by 4
  3. 2024Statistical and Geometrical properties of regularized Kernel Kullback-Leibler divergencecited by 3
  4. 2025Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysiscited by 3
  5. 2025Learning with Differentially Private (Sliced) Wasserstein Gradientscited by 2
  6. 2026Convergence Rates for Distribution Matching with Sliced Optimal Transportcited by 2
  7. 2023Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applicationscited by 1
  8. 2024LaCoOT: Layer Collapse through Optimal Transportcited by 1
  9. 2024Canonical Variates in Wasserstein Metric Spacecited by 0
  10. 2025Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transportcited by 0
  11. 2026Sliced-Wasserstein Distribution Alignment Loss Improves the Ultra-Low-Bit Quantization of Large Language Modelscited by 0
  12. 2026Convergence of empirical subgradients for optimal transport-based objectivescited by 0